Saturday, 19 October 2013

Two Women and a Duck - a Pragmatic case against HFT

This is the last of four articles on the role of reciprocity in financial economics. It develops the case for taking a Pragmatic perspective when trying to understand contemporary finance.

I have presented the case that the essence of the FTAP isreciprocity, alternatively Justice and equality in exchange, colloquially
fairness. The pre-history of mathematical probability lies in Olivi’s
examination of commercial exchange in the context of Aristotle’s Ethics. The subsequent emergence of the topic is
in the seventeenth century analysis of contracts in the context of ‘fair’
pricing. In the twentieth century Ramsey provides the ‘Dutch book’ argument,
which can be viewed as the ‘Golden Rule’ of reciprocity. However, under theinfluence of a strong fact/value dichotomy that was established in the
nineteenth century, the moral injunction not to engage in turpe lucrum, through the practice of arbitrage,
becomes highly technical, and ethically neutral, and in the process the essence
of reciprocity in the FTAP becomes obscured.

This argument associates the FTAP with the experimental results
of the ‘Ultimatum Game’, an important anomaly for neo-classical economics [38]. The game involves two participants and a sum of money.
The first player proposes how to share the money with the second participant.
The division is made only if the second participant accepts the split, if the
first player’s proposal is rejected neither participant receives anything. The
key result is that if the money is not split ‘fairly’ (approximately equally)
then the second player rejects the offer. This contradicts the assumption that
people are rational utility maximising agents, since if they were the second
player would accept any positive payment. Research has shown that chimpanzees
are rational maximisers while the willingness of the second player to accept an
offer is dependent on age and culture. Older people from societies where
exchange plays a significant role are more likely to demand a fairer split of
the pot than young children or adults from isolated communities ([30], [20], [21],
[24]). Fair exchange appears to be learnt behaviour
developed in a social context and is fundamental to human society and
distinguishes the sapient member of a civitasfrom
the sentient animals. The Ultimatum Game provides observational evidence that
reciprocity is, or at least should be, a fundamental concept for financial
economics.

We have shown the key role that the FTAP plays in the dominant
paradigm of financial economics, involving CAPM (Markowitz portfolio
selection), the Efficient Markets Hypothesis (martingales), the use of
stochastic calculus and incomplete markets. At first sight one might assume
that this paradigm associated with utility maximisation, but on closer
reflection the key components are not.

Markowitz portfolio theory explicitly observes that portfolio
managers are not (expected) utility maximisers, as they diversify, and offers
the hypothesis that a desire for reward is tempered by a fear of uncertainty ([26], see also [35, p 432]). Markowitz’s
theory was developed into the CAPM by Sharpe while similar models were
developed independently by Treynor, Lintner and Mossin. These models conclude
that all investors should hold the same portfolio, their individual risk-reward
objectives are satisfied by the weighting of this ‘index portfolio’ in
comparison to riskless cash in the bank, a point on the capital market line.
The slope of the CML is the market price of risk, which is an important
parameter in arbitrage arguments. Significantly, as MacKenzie [25,
pp 86—87] observes, Markowitz portfolio selection and CAPM are prescriptive,
not descriptive theories; just as medieval merchants were told what was licit
by the Scholastics, so, in the 1980s, asset managers were being told what is
‘rational’ by academics.

Merton had initially attempted to provide an alternative to
Markowitz based on utility maximisation employing stochastic calculus. He was
only able to resolve the problem by employing the hedging arguments of Black
and Scholes, and in doing so built a model that was based on the absence of
arbitrage, free of turpe-lucrum. The opening
paragraph of Black and Scholes includes the prescriptive statement that “it
should not be possible to make sure profits”, a statement explicit in the
Efficient Markets Hypothesis and in employing an Arrow security in the context
of the Law of One Price.

Based on these observations, we conject that the whole paradigm
for financial economics, not just the FTAP, is built on the principle of
balanced reciprocity. In order to explore this conjecture we shall examine the
relationship between commerce and themes in Pragmatic philosophy. Specifically,
we highlight Robert Brandom’s position that there is

a pragmatist conception of norms —
a notion of primitive correctnesses of performance implicit in practice that
precludes and are presupposed by their explicit formulation in rules and
principles. [5, p 21]

The argument that we have presented is that reciprocity is
implicit in the practice of commerce (e.g. [22]) and this
norm becomes explicit in Virtue Ethics and then in the early conceptions of
mathematical probability.

The ‘primitive correctnesses’ of commercial practices was
recognised by Aristotle when he investigated the nature of Justice in the
context of commerce and then by Olivi when he looked favourably on merchants.
It is exhibited in the doux-commerce thesis,
compare Fourcade and Healey’s contemporary description of the thesis

Commerce teaches ethics mainly
through its communicative dimension, that is, by promoting conversations among
equals and exchange between strangers. [14, p 287]

the norm of sincerity, the norm of truth-telling, and the norm of asserting only what
is rationally warranted ...[and] is contrasted
with manipulation. [34,
pp 113-114]

There are practices (that should be) implicit in commerce
that make it an exemplar of communicative action.

A further expression of markets as centres of communication is
manifested in the Asian description of a market as “Two women and a duck”,
which immediately brings to mind Donald Davidson’s argument that knowledge is
not the product of a bipartite conversations but a tripartite relationship
between two speakers and their shared environment (e.g. [12]).
The essence of the proverb is that if two women, who are characterised as
talkative, and a duck come together, eventually the value of the duck will be
determined—knowledge is created. Replacing the negotiation between market
agents with an algorithm that delivers a theoretical price replaces ‘knowledge’,
generated through communication, with dogma. The problem with the
performativity that Donald MacKenzie is concerned with [25]
is one of monism. In employing pricing algorithms, the markets cannot perform
to something that comes close to ‘true belief’, which can only be identified
through communication between sapient humans. This is an almost trivial
observation to (successful) market participants (e.g. [37],
[4], [13, especially Ch 12]), but
difficult to appreciate by spectators who seek to attain ‘objective’ knowledge
of markets from a distance.

To appreciate the relevance to financial crises of the position
that ‘true belief’ is about establishing coherence through myriad
triangulations centred on an asset rather than relying on a theoretical model,
consider the comment made by Parliamentary Commission on Banking Standards

Excessive complexity in the major
banks is not restricted to organisational structure. The fuelling of the
financial crisis by misguided risk models was not simply the consequence of
some mathematicians getting their equations wrong. It was the result of
ignorance, coupled with excessive faith in the application of mathematical
precision, by senior management and by regulators. Many of the elements of this
problem remain. [32, para. 93, v. II]

Mathematicians understood the limitations of their models,
which they communicated. The problem was that these concerns were not
appreciated by policy makers, within an institution, nationally or globally,
who appear to have succumbed to the indubitable authority of mathematics [32, para. 60—61, v. II]. Stephen Krasner observes [27] that academics can help policy makers in two
respects: “Provide empirical evidence about what has happened, and offer a
conceptual framework through which to understand it.” A significant issue with
the highly technical mathematical models employed in finance is that they lack
a “conceptual framework” that non-specialists can understand. This means that
policy makers, whether within or without banks, cannot ascertain the
limitations of mathematical models that inform their decision making.
Pragmatism provides the philosophical basis for a conceptual framework that
acknowledges both the usefulness and the fallibility of mathematics in finance.

The significance of these issues to the FTAP is captured in a
text by Rama Cont and Peter Tankov addressing pricing in markets with
discontinuous prices

Unless the martingale measure is a
by-product of a hedging approach, the price given by such martingale measures
is not related to the cost of a hedging strategy therefore the meaning of such
‘prices’ is not clear. [10, 10.5.2]

If the hedging argument cannot be employed, as in the markets
studied by Cont and Tankov, there is no conceptual framework supporting the
prices obtained from the FTAP. This lack of meaning can be interpreted as a
consequence of the strict fact/value dichotomy in contemporary mathematics that
came with the eclipse of Poincaré’s Intuitionism by Hilbert’s Formalism and
Bourbaki’s Rationalism [39]. The practical problem of
supporting the social norms of market exchange has been replaced by a
theoretical problem of developing formal models of markets. These models then
legitimate the actions of agents in the market without having to make reference
to explicitly normative values.

In making this observation and by considering the implications
of believing that the FTAP is an expression of reciprocity, we are employing
the ‘Pragmatic maxim’ and are making a commitment to real-life experiences.
Another, more direct, consequence of associating the FTAP with reciprocity is
related to the EMH. Miyazaki observes [29, p 404] that
speculation by arbitrageurs has been legitimised as ensuring that markets are
efficient. The EMH is based on the axiom that the market price is determined by
the balance between supply and demand, and so an increase in trading
facilitates the convergence to equilibrium. If this axiom is replaced by the
axiom of reciprocity, the justification for speculative activity in support of
efficient markets disappears. In fact, the axiom of reciprocity would
de-legitimise ‘true’ arbitrage opportunities, as being unfair. This would not
necessarily make the activities of actual market arbitrageurs illicit, since
there are rarely strategies that are without the risk of a loss, however, it
would place more emphasis on the risks of speculation and inhibit the hubris
that has been associated with the prelude to the recent Crisis.

These points raise the question of the legitimacy of
speculation in the markets. In an attempt to understand this issue Gabrielle
and Reuven Brenner identify the three types of market participant. ‘Investors’
are preoccupied with future scarcity and so defer income. Because uncertainty
exposes the investor to the risk of loss, investors wish to minimise
uncertainty at the cost of potential profits, this is the basis of classical
investment theory. ‘Gamblers’ will bet on an outcome taking odds that have been
agreed on by society, such as with a sporting bet or in a casino, and relates
to de Moivre’s and Montmort’s ‘taming of chance’. ‘Speculators’ bet on a
mis-calculation of the odds quoted by society and the reason why speculators
are regarded as socially questionable is that they have opinions that are
explicitly at odds with the consensus: they are practitioners who rebel against
a theoretical ‘Truth’ ([6, p 91], [4,
p 394]). This is captured in Arjun Appadurai’s argument that the leading agents
in modern finance

believe in their capacity to
channel the workings of chance to win in the games dominated by cultures of
control ...[they] are not those who wish to “tame chance” but those who wish to
use chance to animate the otherwise deterministic play of risk [quantifiable
uncertainty]”. [1, p 533-534]

In the context of Pragmatism, financial speculators embody
pluralism, a concept essential to Pragmatic thinking (e.g. [33],
[2], [3, Ch 2]) and an antidote to
the problem of radical uncertainty.

Appadurai was motivated to study finance by Marcel Mauss’ essay
Le Don (‘The Gift’), exploring the moral
force behind reciprocity in primitive and archaic societies and goes on to say
that the contemporary financial speculator is “betting on the obligation of
return” [1, p 535], and this is the fundamental axiom of
contemporary finance. David Graeber also recognises the fundamental position
reciprocity has in finance [17], but where as Appadurai
recognises the importance of reciprocity in the presence of uncertainty,
Graeber essentially ignores uncertainty in his analysis that ends with the
conclusion that “we don’t ‘all’ have to pay our debts” [17,
p 391]. In advocating that reciprocity need not be honoured, Graeber is not
just challenging contemporary capitalism but also the foundations of the civitas, based on equality and reciprocity [16, p 235].

The origins of Graeber’s argument are in the first half of the
nineteenth century. In 1836 John Stuart Mill defined political economy as being

concerned with [man] solely as a
being who desires to possess wealth, and who is capable of judging of the
comparative efficacy of means for obtaining that end. [28]

In Principles of Political
Economy of 1848 Mill defended Thomas Malthus’ An Essay on the Principle ofPopulation, which focused on scarcity. Mill was
writing at a time when Europe was struck by the Cholera pandemic of 1829—1851
and the famines of 1845—1851 and while Lord Tennyson was describing nature as
“red in tooth and claw”. At this time, society’s fear of uncertainty seems to
have been replaced by a fear of scarcity (e.g. [23]), and
these standards of objectivity dominated economic thought through the twentieth
century. Almost a hundred years after Mill, Lionel Robbins defined economics as
“the science which studies human behaviour as a relationship between ends and
scarce means which have alternative uses”.

Dichotomies emerge in the aftermath of the Cartesian revolution
that aims to remove doubt from philosophy [3, Ch 1].
Theory and practice, subject and object, facts and values, means and ends are
all separated. In this environment ex cathedra norms,
in particular utility (profit) maximisation, encroach on commercial practice.
This is exemplified by the 1950 English court case Buttle v. Sunders ([1950] 2
All ER 193) where it was judged that ‘my word is my bond’ was subordinate to
the profit maximisation principle.

In order to set boundaries on commercial behaviour motivated by
profit maximisation, particularly when market uncertainty returned after the
Nixon shock of 1971, society imposes regulations on practice. As a consequence,
two competing ethics, functional Consequential ethics guiding market practices
and regulatory Deontological ethics attempting stabilise the system, vie for
supremacy. It is in this debilitating competition between two essentially
theoretical ethical frameworks that we offer an explanation for the Financial
Crisis of 2007-2009: profit maximisation, not speculation, is destabilising in
the presence of radical uncertainty and regulation cannot keep up with
motivated profit maximisers who can justify their actions through abstract
mathematical models that bare little resemblance to actual markets.

This tension is exemplified by the Chartered Financial Analyst
(CFA) Institute Standards of PracticeHandbook[9], where the
primary obligation is to obey the law, where Buttle v Saunders is tempered by
the Basel treaties. There is no discussion of how professionals should interact
amongst themselves, only how they interact with clients and employers, agents
with whom they have a contractual relationship. This suggests that a
distinction is being made between the market, populated by analysts, and
society as a whole.

An implication of reorienting financial economics to focus on
the markets as centres of ‘communicative action’ is that markets could become
self-regulating, in the same way that the legal or medical spheres are
self-regulated through professions. This is not a ‘libertarian’ argument based
on freeing the Consequential ethic from a Deontological brake. Rather it argues
that being a market participant entails restricting norms on the agent such as
sincerity and truth telling that support knowledge creation, of asset prices,
within a broader objective of social cohesion. This immediately calls into
question the legitimacy of algorithmic/high-frequency trading that seems an
anathema in regard to the principles of communicative action.

The purpose of these four posts has been to explore the ethical character
of contemporary financial economics in light of the Financial Crisis of
2007—2008.

By examining the contemporary scholarship on the early development of probability we show that the field emerged in the seventeenth
century out of the ethical assessment of commercial contracts. In the following
century, the doux-commerce thesis dominated discussion of the morality of markets, emphasising the role markets play in
binding society. The ethical aspect of probability theory disappears from
mathematics at the start of the nineteenth century as science replaces
uncertainty with Laplacian determinism [15] and the
self-destructive thesis eclipses doux-commerce.
Economics developed on Mill’s premise that the discipline is “concerned with
[man] solely as a being who desires to possess wealth” and ‘value—neutrality’
emerges, built on the foundation scientific determinism. It was within this
conceptual framework that the Black-Scholes equation was developed.

When a mathematical ‘theory’ to underpin the
Black-Scholes-Merton approach, the Fundamental Theorem of Asset Pricing, is
developed it relies on Kolmogorov’s abstract probabilities. The essence of this
paper is in identifying these ‘martingale measures’ with probabilities that
ensure equality in exchange, implicitly imitating the explicitly ethical
approach of the early probabilists. This observation is significant in that it
provides evidence of ‘oversocialisation’ in a domain traditionally considered
‘undersocialised’.

The argument presented in this post is based on employing the
Pragmatic approach that acknowledges the contingency of knowledge. By taking
this path we argue that markets should be regarded as centres of ‘communicative
action’ governed by Pragmatic norms and that recent financial crises have been
as a consequence of a dissonance between market participants working to
Consequentialist norms but constrained by Deontological norms. In taking this
approach we see a correspondence with Brandom’s semantic pragmatism, firstly
because we see the implicit norm of reciprocity being made explicit in
probability, and secondly because there is a correspondence between the results
of the Ultimatum game, which show humans prefer reciprocity to utility
maximisation and animals do not, and Brandom’s distinction between animal sentinence and human sapience.
This, in turn, offers a solution to the problems of financial regulation.

References

[1] A. Appadurai.
The ghost in the financial machine. Public Culture,
23(3):517—539, 2011.

[2] R.J.
Bernstein. Pragmatism, pluralism and the healing of wounds. In The New Constellation:The Ethical-political Horizons of Modernity/postmodernity,
pages 323—340. MIT Press, 1992.

[28] J. S.
Mill. On the definition of political economy; and on the method of
investigation proper to it. In J. M. Robson, editor, The Collected Works of John Stuart Mill, Volume IV -
Essayson Economics and Society Part I,.
Routledge, 1967.

[29] H. Miyazaki.
Between arbitrage and speculation: an economy of belief and doubt. Historyof Political
Economy, 36(3):369—415, 2007.

2 comments:

This seems very oriented towards Western culture. If you have spent significant time with people from the Middle East, it is very clear that there is very much a sense that in every transaction there is a winner and a loser. Reciprocity is not a central tenet of their trade. That said. I wonder if the end result might be much the same.

This argument is centred on Western culture, but I think their might be connections to Islamic culture, where there are still strict prohibitions on usury. I've worked in the Gulf and my impressions of that area is the society is extraordinarily complex and suspect that intra-cultural norms are very different from inter-cultural norms (i.e. in the Middle Ages there was no prohibition on Jews charging interest to Christians, but there was one on Jews charging interest to Jews).

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About Me

I am a Lecturer in Financial Mathematics at Heriot-Watt University in Edinburgh. Heriot-Watt was the first UK university to offer degrees in Actuarial Science and Financial Mathematics and is a leading UK research centre in the fields.

Between 2006-2011 I was the UK Research Council's Academic Fellow in Financial Mathematics and was involved in informing policy makers of mathematical aspects of the Credit Crisis.